messages listlengths 2 2 | instruction_seed stringlengths 43 1.26k | response_seed stringlengths 43 1.26k | _source stringclasses 1
value | gpt41_mini_response stringlengths 10.4k 40.8k | __original_row_idx int64 58 62.9k | length int64 10.4k 40.8k | ms_id int64 3 3.93k | reasoning sequencelengths 16 16 | deepseek_solution sequencelengths 16 16 | final_reasoning_trace sequencelengths 16 16 | _majority_responses sequencelengths 8 8 | verified_final_reasoning_trace stringlengths 5.58k 66.5k | conversations listlengths 2 2 |
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[{"content":"The polynomial $Q(x) = x^3 + ax^2 + bx + c$ has the property that the sum of its zeros,(...TRUNCATED) | "The polynomial $Q(x) = x^3 + ax^2 + bx + c$ has the property that the sum of its zeros, the product(...TRUNCATED) | "The polynomial $Q(x) = x^3 + ax^2 + bx + c$ has the property that the sum of its zeros, the product(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the polynomial \\( Q(x) = x^3 + a x^2 + b x + c \\), we have the following information:\n\n1.(...TRUNCATED) | 17,177 | 13,227 | 1,073 | ["Okay, let me try to work through this problem step by step. So, we have a cubic polynomial Q(x) = (...TRUNCATED) | ["Given the polynomial \\( Q(x) = x^3 + ax^2 + bx + c \\) with the following conditions:\n1. The sum(...TRUNCATED) | ["<think>\nOkay, let me try to work through this problem step by step. So, we have a cubic polynomia(...TRUNCATED) | ["<think>\nOkay, let me try to figure out this problem step by step. So, we have the polynomial Q(x)(...TRUNCATED) | "<think>\nOkay, let me try to figure out this problem step by step. So, we have the polynomial Q(x) (...TRUNCATED) | [{"from":"human","value":"The polynomial $Q(x) = x^3 + ax^2 + bx + c$ has the property that the sum (...TRUNCATED) |
[{"content":"At what point does the parabola $y = x^2 - 4x + 3$ intersect the circle $x^2 + y^2 = 5$(...TRUNCATED) | "At what point does the parabola $y = x^2 - 4x + 3$ intersect the circle $x^2 + y^2 = 5$? Express yo(...TRUNCATED) | "At what point does the parabola $y = x^2 - 4x + 3$ intersect the circle $x^2 + y^2 = 5$? Express yo(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given:\n\n\\[\ny = x^2 - 4x + 3\n\\]\n\nand\n\n\\[\nx^2 + y^2 = 5\n\\]\n\nWe need to find the point(...TRUNCATED) | 47,067 | 13,661 | 2,941 | ["Okay, so I need to find where the parabola y = x² - 4x + 3 intersects with the circle x² + y² =(...TRUNCATED) | ["To find the points where the parabola \\( y = x^2 - 4x + 3 \\) intersects the circle \\( x^2 + y^2(...TRUNCATED) | ["<think>\nOkay, so I need to find where the parabola y = x² - 4x + 3 intersects with the circle x(...TRUNCATED) | ["<think>\nOkay, so I need to find where the parabola \\( y = x^2 - 4x + 3 \\) intersects with the c(...TRUNCATED) | "<think>\nOkay, so I need to find where the parabola \\( y = x^2 - 4x + 3 \\) intersects with the ci(...TRUNCATED) | [{"from":"human","value":"At what point does the parabola $y = x^2 - 4x + 3$ intersect the circle $x(...TRUNCATED) |
[{"content":"A group of 10 people, each with a different favorite color, are attending a conference.(...TRUNCATED) | "A group of 10 people, each with a different favorite color, are attending a conference. During the (...TRUNCATED) | "A group of 10 people, each with a different favorite color, are attending a conference. During the (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's analyze the problem carefully:\n\n---\n\n**Given:**\n\n- There are 10 people.\n- Each person (...TRUNCATED) | 20,382 | 11,819 | 1,273 | ["Okay, let's try to figure out this problem. So, we have 10 people at a conference, each with a dif(...TRUNCATED) | ["The problem involves 10 people, each with a different favorite color, giving presentations and pro(...TRUNCATED) | ["<think>\nOkay, let's try to figure out this problem. So, we have 10 people at a conference, each w(...TRUNCATED) | ["<think>\nAlright, let's tackle this problem. So, we have 10 people, each with a different favorite(...TRUNCATED) | "<think>\nOkay, so there's this problem about 10 people at a conference, each with a different favor(...TRUNCATED) | [{"from":"human","value":"A group of 10 people, each with a different favorite color, are attending (...TRUNCATED) |
[{"content":"A parallelogram is constructed from two squares with side lengths $a$ and $b$, with one(...TRUNCATED) | "A parallelogram is constructed from two squares with side lengths $a$ and $b$, with one of the squa(...TRUNCATED) | "A parallelogram is constructed from two squares with side lengths $a$ and $b$, with one of the squa(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:** \nWe have two squares with side lengths \\(a\\) and \\(b\\). Construct a (...TRUNCATED) | 17,790 | 14,862 | 1,111 | ["Okay, so the problem is about constructing a parallelogram from two squares with side lengths a an(...TRUNCATED) | ["To solve the problem, we need to determine the ratio of \\( a \\) to \\( b \\) such that the perim(...TRUNCATED) | ["<think>\nOkay, so the problem is about constructing a parallelogram from two squares with side len(...TRUNCATED) | ["<think>\nOkay, so the problem is about constructing a parallelogram from two squares with side len(...TRUNCATED) | "<think>\nOkay, let's see. The problem says that a parallelogram is constructed from two squares wit(...TRUNCATED) | [{"from":"human","value":"A parallelogram is constructed from two squares with side lengths $a$ and (...TRUNCATED) |
[{"content":"A right pyramid is formed from a rectangular base with dimensions 6 cm x 8 cm. The four(...TRUNCATED) | "A right pyramid is formed from a rectangular base with dimensions 6 cm x 8 cm. The four triangular (...TRUNCATED) | "A right pyramid is formed from a rectangular base with dimensions 6 cm x 8 cm. The four triangular (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n\n- Base is a rectangle with dimensions \\(6\\, cm \\times 8\\, cm\\).\n- The pyramid i(...TRUNCATED) | 10,410 | 22,614 | 650 | ["Okay, so I need to find the volume of a right pyramid with a rectangular base that's 6 cm by 8 cm.(...TRUNCATED) | ["To find the volume of the right pyramid with a rectangular base (6 cm x 8 cm) and isosceles triang(...TRUNCATED) | ["<think>\nOkay, so I need to find the volume of a right pyramid with a rectangular base that's 6 cm(...TRUNCATED) | ["<think>\nAlright, let's try to figure out the volume of this pyramid. So, the problem says it's a (...TRUNCATED) | "<think>\nOkay, so I need to find the volume of a right pyramid with a rectangular base that's 6 cm (...TRUNCATED) | [{"from":"human","value":"A right pyramid is formed from a rectangular base with dimensions 6 cm x 8(...TRUNCATED) |
[{"content":"Let $A = (a_{ij})_{3 \\times 3}$ be a square matrix such that the sum of the elements i(...TRUNCATED) | "Let $A = (a_{ij})_{3 \\times 3}$ be a square matrix such that the sum of the elements in each row i(...TRUNCATED) | "Let $A = (a_{ij})_{3 \\times 3}$ be a square matrix such that the sum of the elements in each row i(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given a \\(3 \\times 3\\) matrix \\(A = (a_{ij})\\) with the following properties:\n\n1. The sum of(...TRUNCATED) | 47,265 | 15,259 | 2,954 | ["Okay, so I need to find the sum of all possible values of the determinant of a 3x3 matrix A. The m(...TRUNCATED) | ["Given a 3x3 matrix \\( A = (a_{ij}) \\) such that the sum of the elements in each row is \\( k \\)(...TRUNCATED) | ["<think>\nOkay, so I need to find the sum of all possible values of the determinant of a 3x3 matrix(...TRUNCATED) | ["<think>\nOkay, so I need to find the sum of all possible values of the determinant of a 3x3 matrix(...TRUNCATED) | "<think>\nOkay, let's see. I need to find the sum of all possible values of the determinant of a 3x3(...TRUNCATED) | [{"from":"human","value":"Let $A = (a_{ij})_{3 \\times 3}$ be a square matrix such that the sum of t(...TRUNCATED) |
[{"content":"The polynomial $x^3+ax^2+bx+c$ has three distinct roots, and each root of the polynomia(...TRUNCATED) | "The polynomial $x^3+ax^2+bx+c$ has three distinct roots, and each root of the polynomial is also a (...TRUNCATED) | "The polynomial $x^3+ax^2+bx+c$ has three distinct roots, and each root of the polynomial is also a (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given:\n\n- The cubic polynomial \\(x^3 + a x^2 + b x + c\\) has three distinct roots.\n- Each root(...TRUNCATED) | 42,830 | 17,319 | 2,676 | ["Okay, so I need to find the value of a + b + c for the polynomial x³ + a x² + b x + c, given tha(...TRUNCATED) | ["Given the polynomial \\(x^3 + ax^2 + bx + c\\) with three distinct roots, each of which is also a (...TRUNCATED) | ["<think>\nOkay, so I need to find the value of a + b + c for the polynomial x³ + a x² + b x + c, (...TRUNCATED) | ["<think>\nOkay, so I need to find the value of a + b + c for the polynomial x³ + a x² + b x + c, (...TRUNCATED) | "<think>\nOkay, let's see. The problem says that the polynomial \\( x^3 + ax^2 + bx + c \\) has thre(...TRUNCATED) | [{"from":"human","value":"The polynomial $x^3+ax^2+bx+c$ has three distinct roots, and each root of (...TRUNCATED) |
[{"content":"In triangle $ABC$, we have $\\overline{AD} \\parallel \\overline{CB}$, and $\\overline{(...TRUNCATED) | "In triangle $ABC$, we have $\\overline{AD} \\parallel \\overline{CB}$, and $\\overline{DB}$ interse(...TRUNCATED) | "In triangle $ABC$, we have $\\overline{AD} \\parallel \\overline{CB}$, and $\\overline{DB}$ interse(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n- Triangle \\( ABC \\).\n- \\( \\overline{AD} \\parallel \\overline{CB} \\).\n- \\( \\o(...TRUNCATED) | 46,078 | 16,730 | 2,879 | ["Okay, let me try to solve this geometry problem. Hmm, so we have triangle ABC. AD is parallel to C(...TRUNCATED) | ["Given triangle \\(ABC\\) with \\(\\overline{AD} \\parallel \\overline{CB}\\) and \\(\\overline{DB}(...TRUNCATED) | ["<think>\nOkay, let me try to solve this geometry problem. Hmm, so we have triangle ABC. AD is para(...TRUNCATED) | ["<think>\nOkay, so I need to solve this geometry problem. Let me try to visualize it first. The pro(...TRUNCATED) | "<think>\nOkay, let me try to figure out this geometry problem. So, we have triangle ABC. There's a (...TRUNCATED) | [{"from":"human","value":"In triangle $ABC$, we have $\\overline{AD} \\parallel \\overline{CB}$, and(...TRUNCATED) |
[{"content":"There are 5 circles on a plane, with each circle intersecting exactly 3 other circles. (...TRUNCATED) | "There are 5 circles on a plane, with each circle intersecting exactly 3 other circles. If no more t(...TRUNCATED) | "There are 5 circles on a plane, with each circle intersecting exactly 3 other circles. If no more t(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem Restatement:** \nThere are 5 circles on a plane. Each circle intersects exactly 3 other (...TRUNCATED) | 9,684 | 10,925 | 605 | ["Okay, so I have this problem here: There are 5 circles on a plane, each intersecting exactly 3 oth(...TRUNCATED) | ["To determine the number of intersection points for 5 circles on a plane where each circle intersec(...TRUNCATED) | ["<think>\nOkay, so I have this problem here: There are 5 circles on a plane, each intersecting exac(...TRUNCATED) | ["<think>\nOkay, so I need to figure out how many intersection points there are when there are 5 cir(...TRUNCATED) | "<think>\nOkay, let's try to figure out this problem. So, we have 5 circles on a plane, each interse(...TRUNCATED) | [{"from":"human","value":"There are 5 circles on a plane, with each circle intersecting exactly 3 ot(...TRUNCATED) |
[{"content":"The points A(0,0), B(2,0), C(4,0), D(6,0), and E(8,0) form the vertices of a triangle. (...TRUNCATED) | "The points A(0,0), B(2,0), C(4,0), D(6,0), and E(8,0) form the vertices of a triangle. The point F (...TRUNCATED) | "The points A(0,0), B(2,0), C(4,0), D(6,0), and E(8,0) form the vertices of a triangle. The point F (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n\n- Points \\(A(0,0), B(2,0), C(4,0), D(6,0), E(8,0)\\) lie on the x-axis.\n- They form(...TRUNCATED) | 22,672 | 16,604 | 1,417 | ["Okay, let me try to work through this problem step by step. First, let me make sure I understand t(...TRUNCATED) | ["The problem as stated contains a contradiction since five colinear points cannot form a triangle. (...TRUNCATED) | ["<think>\nOkay, let me try to work through this problem step by step. First, let me make sure I und(...TRUNCATED) | ["<think>\nOkay, so I need to solve this geometry problem. Let me read it again and make sure I unde(...TRUNCATED) | "<think>\nOkay, let's see. We have points A, B, C, D, E all on the x-axis at coordinates (0,0), (2,0(...TRUNCATED) | [{"from":"human","value":"The points A(0,0), B(2,0), C(4,0), D(6,0), and E(8,0) form the vertices of(...TRUNCATED) |
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